Construct rhombus

Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm

Correct answer:

a =  0 cm

Step-by-step explanation:

$$\begin{gathered} 1.AC,\mathrm{\mid }AC\mathrm{\mid }=8cm \\ 2.S;S\in AC,\mathrm{\mid }SA\mathrm{\mid }=\mathrm{\mid }SC\mathrm{\mid } \\ 3.p;p\perp AC,S\in p \\ 4.k;k(S,r=1.5cm) \\ 5.S_1;S_1\in AS,\mathrm{\mid }S{S}_1\mathrm{\mid }=\mathrm{\mid }A{S}_1\mathrm{\mid } \\ 6.S_2;S_2\in SC,\mathrm{\mid }S{S}_1\mathrm{\mid }=\mathrm{\mid }C{S}_1\mathrm{\mid } \\ 7.t_1;t_1(S_1,r=\mathrm{\mid }AS\mathrm{\mid }) \\ 8.t_2;t_2(S_2,r=\mathrm{\mid }CS\mathrm{\mid }) \\ 9.T_1,2;T_1,2=t_1\cap k \\ 9.T_3,4;T_3,4=t_2\cap k \\ 10.A{T}_1;A{T}_2;C{T}_3;C{T}_4 \\ 11.B=A{T}_1\cap C{T}_3 \\ 12.D=A{T}_2\cap C{T}_4 \\ 13.ABCD \\ a=0\text{ cm} \end{gathered}$$

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